I think that a couple of elements need to be made clear at this point. The first would be that Lord Rama never asked anyone to go with him. He insisted that Lakshmana stay back and tend to his mother, Kausalya. At the same time, Lord Rama also insisted on the difficulty of the challenges in living in the forest and for this, Devi Sita should remain in the palace. It is the nature of dharma and how it is viewed that compels Lakshmana to accompany Lord Rama. Lakshmana sees it as his duty to accompany his brother no matter where he goes. At the same time, it becomes clear from the earliest elements that Lakshmana and Lord Rama are closer to one another than the other brothers. It might be due to the fact that Laskhmana represents an avatar of Adi Shesha, the snake that is almost a guardian of Lord Vishnu. The nature of his dharma is one of protectorate and constant companion, the same driving forces of the dharma that Lakshmana cites in going with his brother. Lakshmana is not dismissive about leaving his wife, but rather clear that the dharma to Lord Rama trumps all else. In this, one can see that Devi Sita also views her dharma as devotion to her husband. It is not that Lord Rama "took" her, but rather that she recognized that the highest of fulfillment of her dharma involved being able to accompany her husband. Like Lakshmana, this conception of dharma is something that overwhelemed all else.